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We present a new Certificateless Public Key Encryption (CL-PKE) scheme whose security is proven to rest on the hardness of the Bilinear Diffie-Hellman Problem (BDHP) and that is more efficient than the original scheme of Al-Riyami and Paterson. We then give an analysis of Gentry’s Certificate Based Encryption (CBE) concept, repairing a number of problems with the original definition and security model for CBE. We provide a generic conversion showing that a secure CBE scheme can be constructed from any secure CL-PKE scheme. We apply this result to our new efficient CL-PKE scheme to obtain a CBE scheme that improves on the original scheme of Gentry.